I believe the way the haptic technology is specifically placed and designed vibration motors combined with very, very smart software. The screen wouldn't have to be different. Also, with the way the case tapers, I'd imagine it'd be hard to get a vibration motor in the right place to actually do a haptic home button
However, the haptic claim makes sense, because that, more than anything, explains the thicker case. The iPad 2 had plenty of room in its case (since, hardware wise, it's essentially an iPhone 4S with a bigger battery on the inside). A newer processor that isn't any larger and maybe some extra battery capacity wouldn't explain the added thickness, vibration motors would